Bachelor’s Thesis
Otto Rossi
Simulation of adsorption column for removal of heavy metals from water
18.4.2013
A Redlich-Peterson model constant, m3 kg-1 a particle surface per unit volume of bed, m2 m-3 aBA angular coefficient in BDST model, -
B Redlich-Peterson model constants, m3 kg-1 bBA intersection point in BDST, m-3
CBET BET adsorption isotherm constant, m-3 kg-1 Cid parameter in intraparticle diffusion model, - c concentration in fluid, kg m-3
c0 concentration of initial metal ion solution kg m-3 cb effluent concentration in breakthrough point, kg m-3 ce equilibrium constant of solute, kg m-3
ci interface concentration, kg m-3
cML adsorbate monolayer saturation concentration, kg m-3 cs adsorbate concentarion in solids, kg m-3
Deff effective diffusivity, m2 s-1 Dm diffusivity in the fluid, m2 s-1 Ds diffusivity in the solid, m2 s-1 dp particle size, m
g dimensionless Redlich-Peterson parameter, - Ka Langmuir constant, m3 kg-1
KBA rate constant in BDST model, kg-1 s-1 Kd distribution coefficient of the adsorbate, - Kf Freundlich constant, kg1-1/n kg-1
k1 pseudo-first order diffusion rate constant, 1 s-1 k2 pseudo-second order rate constant, kg kg-1 s-1
kf the external mass transfer coefficient between the fluid and the particles in packed bed, m s-1
kid intra-particle diffusion rate constant, kg kg-1 s-0,5
m initial adsorption rate in Elovich equation, kg kg-1 s-1 n Freundlich parameter, -
mean value of the concentration in the particle, kg kg-1 qb adsorption capacity in breakthrough point, kg kg-1 qe adsorption capacity at equilibrium, kg kg-1
qi concentration of the solids at the interface, kg m-3 qm Langmuir monolayer capacity, kg kg-1
qt adsorption capacity at any timet, kg kg-1 R gas constant, J mol-1 K-1
Rep particle Reynolds number, - r particle radius, m
Sc Schmidt number, -
Sh Sherwood number, -
T temperature, K
t time, s
tb breakthrough time, s tst stoichiometric time, s
u superficial velocity in the bed, m s-1
uE desorption constant in Elovich equation, kg kg-1 volumetric flow rate, m3 s-1
Vb effluent volume in breakthrough point, m3
mass transfer rate in the unit volume of bed, kg m-3 s-1 z location in the column, m
G Gibbs free energy, J mol-1 H change in enthalpy, J mol-1 S change in entropy, J mol-1 K-1
porosity of the bed, -
f density of the fluid, kg m-3
s density of the solid, kg m-3
2 ADSORPTION OF HEAVY METALS ... 5
2.1 Different types of adsorption mechanisms ... 5
2.2 Adsorption mechanisms of heavy metals ... 6
3 ADSORBENT MATERIALS ... 8
3.1 Activated carbon ... 9
3.2 Silica gel and hydrogels ... 11
3.3 Activated alumina ... 12
3.4 Nanosized metallic oxides ... 13
3.5 Zeolites and clay... 14
3.6 Biosorbents ... 15
3.7 Industrial wastes ... 16
4 REGENERATION OF ADSORBENTS ... 17
5 ADSORPTION EQUILIBRIA ... 20
5. 1 Adsorption isotherms for single-component equilibria ... 21
5.1.1 Freundlich adsorption equation ... 22
5.1.2 Langmuir adsorption equation ... 23
5.1.3 Redlich-Peterson model ... 24
5.1.4 BET equation ... 24
5.1.5 Other adsorption isotherms ... 25
5.2 Adsorption kinetics... 25
5.2.1 Modeling adsorption ... 25
5.2 Kinetics model used ... 25
5.2.1 Pseudo-first order kinetic model ... 26
5.2.2 Pseudo-second order kinetic model ... 26
5.2.3 Intraparticle diffusion kinetic model ... 27
6 FACTORS AFFECTING ADSORBTION EQUILIBRIA ... 29
6.1 Effect of pH... 29
6.2 Effect of initial metal ion concentration ... 32
6.3 Effect of temperature ... 33
6.4 Mode of operation ... 36
6.5 Effect of agitation speed and flow rate ... 36
6.6 Other factors affecting adsorption equilibria ... 37
7 SIMULATION OF AN ADSORPTION COLUMN ... 38
7.1 General procedure of design ... 38
7.1.1 Length of Unused Bed ... 39
7.1.2 Bed Depth Service Time Model ... 40
7.1.3 Empty Bed Residence Time model... 41
7.2 Mass transfer modeling ... 42
7.2.1 Basic equations for adsorption column ... 42
7.2.2 Analytical solutions for breakthrough curve ... 45
7.2.3 Numerical solution for breakthrough curve ... 46
7.2.3 Parameters for simulation ... 46
7.3 Simulation results ... 48
8 CONCLUSIONS ... 52
REFERENCES ... 54
1 INTRODUCTION
Heavy metals are found in natural waters and especially in industrial effluents.
For example copper can cause damage to the brain, liver and some other internal organs. Excessive ingestion of copper can cause vomiting and cramps, or even death [1]. Heavy metals like cadmium and lead tend to accumulate in living organisms and they pose a serious risk for humans and environment. Chronic exposure of cadmium can cause kidney dysfunction and lead can cause central nerve damage. Lead can damage kidney, liver and brain functions [2]. For this reason the level of these pollutants in industrial wastewaters are strictly regulated by authorities and the demand of removing heavy metals from water and wastewater is ever increasing. Some permissible limits for potable water are represented in Table I.
Table I. Word Health Organisation’s and EU’s drinking water standards for selected heavy metals [3 W].
WHO, mg/L EU standard, mg/L
Cadmium 0.003 0.005
Copper 2 2.0
Lead 0.01 0.01
Conventional methods of removing heavy metal from aqueous solutions include chemical precipitation, ion exchange, membrane processes, adsorption and electrochemical treatment technologies etc. [2]. Chemical precipitation is the most widely used in industry but it is inefficient in low concentrations and the disposal of the forming sludge is an issue. Adsorption offers flexibility in design and operation and in many cases it will generate high-quality treated effluent. In addition, adsorbents can be often regenerated and heavy metals can be even recovered. The interest in heavy metal removal by adsorption can be seen from numerous studies aiming to find efficient and inexpensive adsorbent material. The major advantages and disadvantages of the most common heavy metal removal technologies are represented in Table II.
Table II. Conventional heavy metal removal technologies [4, 5]
Method Disadvantage Advantage
adsorption adsorbents require regeneration flexibility and simplicity of design, ease of operation and insensitivity to toxic chemicals
chemical precipitation
pH dependence difficult separation
adverse effect by complexing agent resulting sludges
chemicals required
simple and cheap
ion exchange sensitive to particles high operation cost
no selectivity to alkaline metals metallic fouling
pure effluent
pure effluent metal recovery possible
membrane membrane fouling limited life of membrane expensive
high pressure
pure effluent
flocculation coagulation
chemicals required (electrolytes) generate very fine particles of precipitates flotation less selective for heavy metals cost competitive to
precipitation electrodialysis takes time
large electrode surface are required fouling
expensive
metal selective
Although adsorption processes are relatively easy to model and design, many methods presented in the literature require simplifying assumptions or need experimental data to be valid. The purpose of this study is to simulate and design an adsorption column for purification of heavy metals from water with an easy method requiring limited amount of information from literature. The study is focused on the removal of Cu2+, Pb2+ and Cd2+ ions from waters and from wastewaters. Adsorption of heavy metals and suitable adsorbents are discussed in the first part of this paper. Other topics discussed are regeneration of adsorbents and some basic adsorption equilibria and kinetics are introduced. The latter part of
this paper is a case study focused on the simulation and design of adsorption column by using software developed by Reunanenet al. [6].
2 ADSORPTION OF HEAVY METALS
In adsorption the molecules distribute themselves between two phases, one of which is a solid and the other is either a liquid or a gas [7]. Due to the nature of heavy metals, only liquid adsorption can be used for heavy metal removal from waters and wastewaters.
2.1 Different types of adsorption mechanisms
Adsorption may be classified as physical adsorption and chemisorption. In the first one the adsorption forces are relatively weak, consisting of mainly van der Waals forces and supplemented in many cases by electrostatic contributions from field gradient-dipole or –quadrople interactions. In chemisorption there is a significant electron transfer, which is equivalent to the formation of a chemical bond between the sorbate and the solid surface. Those interactions are stronger and more specific than in physical adsorption but they are limited to monolayer coverage of the solid surface. Summary of differences between physical adsorption and chemisorption is presented in Table III. [8, 9]
Table III Classifications of adsorption according to [9].
Parameter Physical adsorption Chemisorption
heat of adsorption low, < 1-5 times latent heat of evaporation
high, > 1-5 times latent heat of evaporation
specificity nonspecific highly specific
nature of adsorbed phase
monolayer or multilayer, no dissociation of
adsorbed species
monolayer only, may involve dissociation temperature range only significant at
relatively low temperatures
possible over a wide range of temperature forces of adsorption no electron transfer,
although polarization of sorbate may occur
electron transfer leading to bond formation between sorbate and surface reversibility rapid, non-activated,
reversible
activated, may be slow and irreversible
2.2 Adsorption mechanisms of heavy metals
Adsorption mechanism varies greatly depending on the adsorbent material and conditions of the adsorption (mainly pH) and adsorbent used. The more detailed discussion of pH is described in later chapters. However, it should be mentioned that heavy metals exist in various forms in water depending on the pH. They are present in aqueous solutions as hexaqua complex ions with six surrounding water molecules [10].
Lyubchik et al. [11] suggested that there are different mechanisms for copper adsorption on oxidized and non-oxidized activated carbons. The oxidizing of activated carbon is a chemical treatment to improve the adsorption properties of the adsorbent (in this case, 1M HNO3 was used). In their study they concluded that the electrostatic interactions (attraction or repulsion) do not seem to have an important effect on the adsorption of the metal on oxidized activated carbons from co-mingled wastes. Mechanism plausible consisted of first fast ion-exchange of the aqueous metal ions (1) and (2), followed by their surface hydrolysis (3) and slower chemisorption and finally outer-sphere complexation that converts inner- sphere complexation with time (4). The latter two reactions could occur in series or parallel. The cation exchange mechanism with carboxylic group is presented in Figure 2. The denotations RxCOOH represents carboxylic groups (or quinone group) attached in the activated carbon, Me stands for metal.[11]
2( ) + = 2( ) + 2 (1)
+ ( ) = ( ) + (2)
[ ] + [2 ] (3)
+ ( ) = … ( ) + (4)
Kumaret al. [12] 2007 postulated that coordination bond formation with amine (- NH2) group of aniline formaldehyde coated silica gel as the adsorption mechanism. In the presence of mineral acids, the NH2-group was protonated and good desorption occurred. Barakat [13] investigated adsorption behavior of copper to hydrous TiO2-adsorbent. Adsorption takes place via the formation of – Cu bonding, like presented in the Figure 1. It was also concluded that this is the main mechanism of hydrous metallic oxide adsorption.
Figure 1. The adsorption mechanism of Cu(II) on hydrous TiO2. [13]
Barakat [14] reviewed briefly the adsorption mechanisms of modified agriculture and biological wastes (biosorbents) in his study. The adsorption can take place by metabolism-independent metal binding to the external surfaces and cell walls.
Adsorption involves ionic, chemical and physical adsorption. Various ligands located on the fungal walls take part in metal chelation. These include carboxyl, hydroxyl, amine, sulfhydryl and phosphate groups. Metal ions are capable of forming complexes with negatively charged reaction sites on the cell wall surface.
Polysaccharide material (modified biopolymers) adsorption mechanism differs greatly from other conventional materials due to its complexity in structure.
Biopolymers possess number of different functional groups. Two different mechanisms (chelation versus ion exchange) may involve in metal complexation of chitosan. This is dependent of pH. Chitosan characteristically has many amine groups that are responsible for metal ion binding by chelation. In acidic solutions chitosan is protonated and has electrostatic properties. It can therefore also act as an anion exchanger. Adsorption mechanism in hydrogels is basically governed by
diffusion of water into the hydrogel and the metal ions are trapped inside. This is especially true in the absence of strongly binding sites. [14]
According to Erdem et al. [10] adsorption mechanism by natural zeolite is attributed to different mechanisms of ion-exchange processes and adsorption process. Metal ions have to move through channels of the lattice (see Chapter 3.5 for details) and replace the exchangeable cations during the ion-exchange process.
The hydrated metal ions were roughly the same size according to measurements, which meant that the exchange may occur via difficulty [10]. This topic was not discussed further in the study, which meant probably that the adsorption mechanism wasn’t known in detail. The mechanisms of zeolite adsorption in general differ greatly from other mechanisms.
Figure 2. Cation exchange mechanism with the carbon surface carboxylic group [15].
In some cases it’s even possible that precipitation of certain heavy metal may occur and result interesting adsorption behaviors. Turan et al. [16] reported that lead precipitated on the surface clinoptilolite (natural zeolite) as lead hydroxide.
It was debatable if the precipitation occurred in the surface of the adsorbent or only in the solution because of the poor solubility of lead hydroxide. Precipitation was considered a major lead removal affecting factor in the system.
3 ADSORBENT MATERIALS
An adsorbent, according to Richardsonet al. [7], has to meet certain requirements in order to be commercially attractive:
it should have a large internal area.
the area should be accessible through pore big enough to admit the molecules to be adsorbed. It is a bonus if the pores are also small enough to exclude molecules which it is desired not to adsorb.
the adsorbent should be capable of being easily regenerated
the adsorbent should not age rapidly, that is lose its adsorptive capacity through continual recycling.
the adsorbent should be mechanically strong enough to withstand the bulk handling and vibration that are a feature of any industrial unit.
A practical adsorbent in liquid separation on the other hand has according to Kirk- Othmer [8] four primary requirements: selectivity, capacity, mass transfer rate, and long-term stability. These requirements are discussed below for the most common adsorbents and some newer ones.
3.1 Activated carbon
Activated carbon can be manufactured from naturally occurring carbonaceous materials such as wood, coal, coconut shells or bones decomposed in an inert atmosphere at a temperature of around 800 degrees. The product is not porous and needs additional activation by processes referred as chemical activation or gas activation. [17]
A typical surface area for activated carbon is around 1000 m2/g [7], although much higher values can be achieved [8], but these very high surface area carbons tend to lack physical strength which hinders their practical use. Activated carbon can be used as powder (PAC) or in granular form (GAC). The granular form is used mostly for gas adsorption and powder is the preferred option for liquid adsorption. Liquid-phase, or decolorizing, carbons are generally fluffy powders with surface area of around 300 m2/g and the pore size is usually 3.0 nm or larger, which enables faster diffusion [17]. The particle size of granular activated carbon is usually greater than 0.1 mm [18]. In some cases it’s even possible to utilize carbon molecular sieves (CMS) or activated carbon fibers (AFCs) [19], which both have relatively narrow micropore size distribution.
Figure 3. Scanning electron micrograph (SEM) of activated carbon (a) before (b) after treatment [20].
To name some studies, Uzun and Güzel [21] have studied adsorption of some heavy metal ions from aqueous solution by activated carbon and Marinkovski et al. [22] concentrated their studies on granular activated carbon (adsorption capacity for Cd2+ and Pb2+, 20.1 and 17.9 mg/g; respectively). An et al. [23]
obtained adsorption capacities for Pb2+, Cu2+ and Cd2+ ions for several adsorbents.
Adsorption capacities were for PAC 26.9, 4.4 and 3.4 mg/g and for GAC 16.6, 5.1 and 3.4 mg/g; respectively. Dwivedi et al. [18] got similar results for GAC for Pb2+ with adsorption capacity of 26.5 mg/g. Leyva-Ramos et al. [24] investigated adsorption of Pb2+ on various types of activated carbon fibers and received the best adsorption capacity of 36.6 mg/g. Due to the relative expensiveness of activated carbon there are a lot of studies trying to manufacture a cheap adsorbent materials. Lyubchik et al. [11] are one of them by converting waste into activated carbon and studying heavy metal removal from wastewater. Goel et al. [20] are one of the many to investigate the modifications of activated carbon (granular).
The properties of unmodified and modified were studied. The treated activated
carbon showed 35% increase in uptake capacity of lead ions. The surface of the activated carbon before and after treatment is shown in Figure 3.
3.2 Silica gel and hydrogels
Pure silica, SiO2, is a chemically inactive non-polar material but when it has a hydroxyl group (silanol group), its surface becomes very polar and hydrophilic.
The surface area of silica gel varies from 100 to over 800 m2/g. The product is provided in granular and spherical forms. Pore sizes are typically from 2.0 - 16 nm [17]. Due the silica-gel surface has an affinity for water and organics, the primary adsorptive application of silica gel is the dehydration of gases and liquids.
Silica gel doesn’t belong to the most attractive heavy metal removal adsorbents and there aren’t many recent studies. Tran and Roddick [25] investigated adsorption of lead ions on fixed beds with silica gel and the use of silica gel as carrier have occurred in many studies, such as Kumar et al. [12] research of uptake and desorption of copper ion using functionalized polymer coated silica gel in aqueous environment. The obtained adsorption capacity for Cu(II) was 76.3 mg/g.
According to Lyubchik et al. [26] Hydrogels are polymeric materials having carboxylic acid, amide, amine or ammonium groups which can bind heavy metal ions. Hydrogels tend to swell by the ionic strength, pH and temperature the same way as silica gel does. Figure 4 shows a schematic representation of polymerization and crosslinking reaction. It results a three-dimensional network formation of cationic hydrogel. The main problem with these adsorbents is their durability, which is not at the level of commercialization.
Figure 4. Three-dimensional formation of cationic hydrogel. [26]
Krusicet al. [27] studied poly(acrylamide-co-sodium methacrylate) hydrogels for Pb2+ adsorption (adsorption capacity 68.9 mg/g). Wang et al. [28] researched poly(polyethylene glycol diacrylate) and poly(methylacrylic acid) adsorbents.
Adsorption capacities for Pb(II), Cu(II) and Cd(II): 114.0, 22.9, 37.1 and 466.2, 78.8, 121.4 mg/g, respectively, were obtained. Wang et al. [29] compared adsorption capacity of new hyper-crosslinked polystyrene adsorbent to two commercial adsorbents. The new sorbent achieved capacity of Cu2+ removal of 126.6 mg/g, which was noticeably higher than the commercial ones.
3.3 Activated alumina
Aluminum oxides have several crystal forms. Activated alumina that is used as adsorbent is mainly -alumina. Porous alumina is produced by dehydration of alumina hydrates. Typical specific surface areas range from 200 to 500 m2/g and the predominant pore diameter is in the 2 - 5 nm range. Activated alumina cannot compete in terms of capacity and selectivity to for example molecular sieve zeolites. One of the biggest assets is the durability of the material and activeated alumina is widely used in moving-bed applications. The most important industrial applications are found in drying processes for both liquids and gases. [17]
Figure 5. Scanning electron micrographs (SEM) of activated alumina (500x).
[30]
Liuet al. [31] conducted a study of adsorption of copper(II) and chromium(IV) on diaspora, which is a naturally occurring aluminum oxide. Adsorption capacity of 1.9 mg/g for copper ions was achieved. Activated alumina was the subject of the study by Naiya et al. [30] (surface of the adsorbent shown in Figure 5) and they obtained adsorption capacities of 35.1 and 83.3 mg/g for Cd(II) and Pb(II), respectively.
3.4 Nanosized metallic oxides
Most widely studied nanosized metal oxides (NMOs) for heavy metal removal include aluminum, iron, manganese and titanium oxides. The size and shape of NMOs varies and they are both important factors affecting adsorption performance. Particle size of NMOs vary from 2 to several hundreds of nanometers (latter number for needlelike particles) and surface area is in the range of 25 – 400 m2/g. NMOs provide an effective and specific heavy metal adsorption.
They exist as fine or ultrafine particles, which causes problems due to agglomeration, difficult separation and excessive pressure-drops when used in flow-through systems. To overcome these problems there is a lot of research going on in the field of manufacturing NMOs and fabricating them by impregnating or coating NMOs particles into porous supports of larger size. These supports include natural hosts such as bentonite and sand, metallic oxide materials, such as Al2O3 membrane, and porous manganese oxide complex and synthetic polymer hosts, such as cross-linked ion-exchange resins. However the use and
fabrication of NMOs is still in development stage and various issues needs to be solved before commercial use. [32]
Huaet al.[32] listed some typical values for heavy metal removal with nanosized metallic oxides. For lead ions the values varied from 9.2 to 324.3 mg/g (the highest for hydrous manganese oxide), for copper ions values ranged from 15.4 to 1600 mg/g (the highest value for zinc oxide) and for cadmium ions values ranged from 7.9 to 143.3 mg/g (hydrous manganese oxide as the top value).
3.5 Zeolites and clay
Zeolite is an aluminosilicate mineral which is formed in hydrothermal conditions.
Zeolites can be found naturally but they can also be produced industrially. More than 40 kinds of zeolite have been found in natural mines but oddly more than 150 different types can be made synthetically. [17]
Because of the regular crystalline structure, zeolites provide unique adsorption characteristics and adsorbents with very narrow pore size distribution are possible.
The adsorption takes places within the crystals, in which the access is limited by the pore size. Zeolites can therefore selectively adsorb or reject molecules based on their molecular size which is called the molecular-sieve effect. The adsorption in zeolites cannot be explained with traditional theories of adsorption. [17]
An et al. [23] compared several adsorbents in their study relating adsorption capability of crab shells. They got heavy metal uptakes of zeolite for Pb, Cu and Cd: 111.9, 14.6 and 30.4 mg/g; respectively. Erdem et al. [10] investigated removal of heavy metal cations by natural zeolites and got a result of 9.0 mg/g adsorption capacity for Cu(II) removal with natural zeolite. Marinkovskiet al. [22]
obtained adsorption capacities for natural zeolite for Cd2+ and Pb2+ with results of 18.4 and 18.7 mg/g, respectively.
Clay minerals are being studied for heavy metal removal. There are three different types of clay: montromorillonite, bentonite and kaolinite. Among clay minerals the first two have shown reasonable removal for Cu(II). Compared with adsorbents from agricultural wastes, the price of these materials is relatively higher. [33]
Kurniawan et al. [33] reported several heavy metal uptakes by unmodified and modified natural materials, some of which are listed in the Table IV.
Table IV. Some adsorption capacities of heavy metals on natural materials. [33]
Adsorption material
Adsorption
capacity of Cu2+, mg/g
Adsorption
capacity of Cd2+, mg/g
Natural zeolite 25.04 -
HCl treated clay 83.3 -
Kaolinite 1.9 - 10.79 0.75 - 4.47
Modified kaolinite 4.8 8.6
Ball clay 3.0 2.24
Bentonite 9.27 18.16
Diatomite 3.24 5.54
Montmorillonite 3.04 5.20
Gupta and Bhattacharyya [34] studied 6 different kind of clays with modifications and they obtained adsorption capacities between 9.0 to 31.4 mg/g for Pb(II). The value for unmodified clay was 11.5 mg/g. Bhattacharyya and Gupta and [35] got adsorption capacities (in the same conditions and with same adsorbents as the study mentioned earlier) between 3.0 to 28.8 mg/g for Cu(II).
3.6 Biosorbents
According to Cho et al. [4] biosorption is a process that utilizes dead biomass to remove toxic heavy metals. Biosorbents are prepared from waste biomass of industry or from suitable natural sources. One special case of this is use of microbial biomass such as different types of bacteria, algae and fungi. The binding capacities of some biomass can be compared with the commercial cation exchange resins. The biosorption has not been commercialized, although the research has been extensive for decades according to Wang and Chen [36]. The writers were skeptical if the biosorbents would have any competition in many types of industrial scale metal removal applications.
Singhtet al. [37] studied use of filamentous algeaPithopora oedogonia for Cu(II) and Pb(II) removal from aqueous solution with adsorption capacities of 23.1 and 71.1 mg/g, respectively. The results were compared with some other biosorbent studies. Adsorption capacities for Cu(II) were 18.8 – 23.3 mg/g with unicellular algea, 29.3 mg/g with seaweed and 8.7 – 133.3 mg/g with other filamentous algae.
Comparison to lead ions removal uptakes were 97.4 mg/g for unicellular algae, 54.0 – 229.0 mg/g for seaweeds and 31.1 – 198.5 mg/g for filamentous algae.
3.7 Industrial wastes
Some industrial wastes such as fly ash, blast furnace slag and sludge, red mud, lignin and waste slurry etc. are currently being researched as potential low-cost adsorbents to remove heavy metal from wastewater. Ahmaruzzaman [5]
conducted a study on these low-cost adsorbents and found out that modified industrial wastes showed high adsorption capacities. It was concluded that removal of heavy metals with industrial wastes as adsorbents poses few drawbacks similar to biosorbents, such as lack of study on utilization of them in commercial scale. The review indicated need for further study on several aspects such as column studies, regeneration and adsorption mechanisms in detail [5].
Kurniawanet al. [33] published a comparison of low-cost adsorbents for treating wastewaters laden with heavy metals and it was evident that adsorbents from industrial waste demonstrate outstanding capabilities for the removal of heavy metals. Some adsorption capacities of industrial wastes are presented in Table V.
Technical applicability and cost-effectiveness were said to be the key factors for selection of the most suitable adsorbent.
Table V. Some adsorption capacities of industrial by-products or wastes [33 ].
Adsorbent material
Adsorption capacity of Cu2+, mg/g
Adsorption capacity of Cd2+, mg/g
Adsorption
capacity of Pb2+, mg/g
Waste slurry 20.97 15.76 1030
Red mud 106.44 66.67 -
Lignin 6.7 – 22.87 6.7 - 25.40 8.2 – 1865
4 REGENERATION OF ADSORBENTS
Loaded adsorbents can be regenerated by temperature- or pressure-swing processes [38], but this is not the case with heavy metals. Other methods are displacement and extraction. Acid solutions are the preferred desorption agent to desorb heavy metal ions from the adsorbent.
Wang et al. [29] used 2% HCl (hyper-crosslinked polystyrene adsorbent, Cu2+), which effectively desorped the adsorbent. The cycle was repeated for 5 times with desorption efficiencies varying from 93.3 to 96.8% and the breakthrough time decreased insignificantly. Guptaet al. [39] used 3M HNO3 (activated carbon from fertilizer waste, Pb2+) with 88% recovery in the first desorption cycle. However, the adsorption capacity declined almost 50% until the end of the sixth regeneration cycle. Singh et al. [40] conducted five sorption-desorption cycles using 0.1 M HCl (Pithophora biomass, Cu2+ and Pb2+). The adsorption decreased 41% for Cu(II) and 25% for Pb(II) removal. The results are shown in Figure 6 and they were average compared to some other studies with biosorbents. Biomass loss of 10 - 15% was recorded at the end of the regeneration cycles. Krusicet al. [27]
used 0,01 M HNO3 (hydrogel, Pb2+) and their desorption studies suggested that the adsorption was realized mainly by electrostatic attraction. The adsorption capacity did not show significant changes after multiple recycles. Wanget al.[28]
got promising results for hydrogel desorption. Desorption was higher than 96%
and after three cycles, desorption rate did not alter significantly.
Figure 6. A typical results for regeneration study: Adsorption and desorption cycles of Cu(II) and Pb(II) by Pithopohora. Adsorption initial concentration 100 mg/L, temperature 25°C, time 30 min, biomass concentration 1 g/L. 0.1 M HCl was used as desorbing agent [40].
Kumar et al. [12] studied desorption more widely on functionalized polymer coated silaca gel. Desorption of copper ions was carried out by using four types of desorbents (HCl, H2SO4, HNO3, EDTA). The equilibrium was achieved in 40 minutes in the batch study. 0.2 M HCl resulted 72% and 0.002 M EDTA resulted 62% of maximum desorption. With 1 M mineral acids and 0.2 M EDTA desorption efficiencies were all in the range of 97 - 100%. The removal of heavy metals from adsorbent was claimed to be due to the protonation of amine groups.
Granular activated carbon in packed bed column was studied for Pb(II) removal by Dwivedi et al. [18]. Use of high concentration nitric acid was addressed to provide better results for desorption because the high concentration of HNO3 equals to higher quantity of exchangeable H+ ions. However, in actual elution process, it may result serious problems occurred in the disposal of the highly
acidic effluent. For this reason the desorption studies were conducted with 0.5 M HNO3.
Column studies differ from batch studies: in batch studies, the system reaches equilibrium in the flask, whereas in the column the fresh eluent is fed to the column continuously. An example of desorption in column is presented in Figure 7. At first the effluent concentration increased rapidly, until it starts to decline and, in this case, desorption was negligible after 1 hour. In columns the amount of desorbing agent is often optimized and like in the study by Kumar and Bandyuopadhyay [41] the column was operated in counter-current mode (opposite direction of adsorption). The flow rate was also decreased slightly to improve desorption economy.
Figure 7. Desorption of Cd(II) from treated rice husk [41].
Desorption studies can reveal a lot from the adsorption mechanism of studied adsorbent. In some cases it is possible, for example, to get information of the percentage of chemical adsorption versus physical adsorption with the aid of adsorption and desorption studies. [12]
In some cases the regeneration may give better results for adsorption for at least during the first couple of desorption cycles. For example this was observed in the regeneration study by Katsou et al. [42] with natural zeolite. Multiple reasons were speculated: removal of impurities from channels of zeolite, modification of used KCl solution by replacing ions originally in the material, formation of complexes among chlorides and metals.
5 ADSORPTION EQUILIBRIA
The adsorption equilibrium is the phenomenon when the rate which molecules are adsorbed is equal to the rate of which they are desorbed. There are many theories to describe the phenomena but none of them fully explain the physical and chemical effects occurring in adsorption. Fortunately, for engineers it is not relevant to know all the details in order to calculate the process in a satisfactory level. For this reason most of the theories developed in earlier stages are still very useful, although some of the assumptions in them are not entirely valid. Most of the theories are developed for gas-adsorption mainly because the gaseous state is better understood than liquid. Part of this behavior is explained by the lack of industrial applications in liquid processes. [7]
The adsorption equilibrium is described mainly by the relation between the concentration of a component in the fluid phase and its loading on the adsorbent.
For liquid adsorption of heavy metals, the amount of component in the fluid is normally expressed as a molar or mass concentration (moles per liter or grams per liter). The absorbent loading is represented either by mass loading (milligrams of adsorbate per gram of adsorbent) or mole loading (moles of adsorbate per grams of adsorbent). The most common way to represent adsorption equilibrium is to keep the temperature constant and plot concentration of metal ion at equilibrium Ce against adsorption capacity in equilibrium qe to give an adsorption isotherm.
An example is presented in Figure 8. Other possibilities are for instance keeping Ce constant gives adsorption isostere. In gas-liquid systems the pressure can be kept constant to obtain adsorption isobar. [7]
Figure 8. Adsorption isotherms of Cu2+ on WJN-101 (new cross-linked polystyrene adsorbent) at different temperatures [29].
5. 1 Adsorption isotherms for single-component equilibria
Singe-component adsorption isotherms can be generally characterized by some typical curves (I-V), which are shown in Figure 9. The type I is the most favorable and the type III is unfavorable. It should be noted that some of these types do not exist in liquid adsorption systems. These isotherms are often described by some equations presented in the following chapters.
Figure 9. Classification of isotherms into five types according to Brauner, Deming, Deming and Teller [7].
5.1.1 Freundlich adsorption equation
The Freundlich adsorption equation is one of the most used mathematical expressions to describe an adsorption system. It is expressed as
= ( ) (5)
where qe adsorption capacity at equilibrium Kf Freundlich constant
n dimensionless Freundlich parameter Ce equilibrium constant of solute.
To linearize the data, the Freundlich equation is written in mathematical form
log = log + log (6)
Kf describes Freundlich adsorption capacity and the dimensionless exponent n denotes the favorability of adsorption (0<n<10 favorable).
5.1.2 Langmuir adsorption equation
The Langmuir adsorption equation is described by equation
= (1 + ) (7)
where Ka Langmuir constant
qm Langmuir monolayer capacity.
Equation (7) assumes that rate of adsorption is proportional to the empty surface available as well as to the fluid concentrations. The equation is valid until monomolecular coverage and it assumes that there are no interactions between the molecules on the surface and the energy of adsorption is the same all over the surface.
Although the model assumptions, it can be used for situation where the assumptions are not valid. The equation is probably the most used adsorption isotherm in liquid adsorption of heavy metals. Typical adsorption isotherms for the selected heavy metal removal are presented in Figure 10.
Dimensionless separation factor (known as constant separation factor or equilibrium parameter)RL describes the favorability of the adsorption:
= (1 + ) (8)
where c0 concentration of initial metal ion solution.
Values between 0 <RL< 1 indicate favorable reaction process, RL= 0 irreversible case,RL= 1 linear case and R> 1 unfavorable reaction. [43]
Figure 10. Adsorption isotherm of Pb(II), Cu(II) and Cd(II) on MDA-SBA-15 (a) Langmuir and (b) Freundlich at the adsorbent dose of 1 g/L, pH 4.0 and temperature of 25°C [44].
5.1.3 Redlich-Peterson model
Redlich-Peterson model (R-P) [45] is presented (according to [46]) in the form:
= (9)
where A,B R-P model constants
g dimensionless R-P parameter.
The parameter g should be in the range of 0 to 1.0. For g = 0 and g = 1, the equation is analogous to Henry’s law and to Langmuir equation, respectively.
5.1.4 BET equation
Another common adsorption equation was presented by Brauner, Emmet and Teller (BET) [47]. The equation is written in form (according to [46 ]):
=( )[ ( )( ) (10)
where cML adsorbate monolayer saturation concentration CBET BET adsorption isotherm constant
qs theoretical adsorption isotherm capacity.
The details of the validity of this equation are not discussed here. However, it can be used to describe multilayer sorption and it can represent all the five types of adsorption isotherms.
5.1.5 Other adsorption isotherms
In the literature there are several other ways to describe single component adsorption isotherms. Ahmaruzzamann [5] has listed several cases used in articles for single and multicomponent adsorption models reported in the literature. For single-component adsorption there are also Sips Isotherm, Radke-Prausnitz, Frenkel-Halsey-Hill (FHH), Tempkin, Toth, Flory-Huggins, Koble-Corrigan, MacMillan-Teller (MET), Dubinin-Radushkevich and Khan isotherm types.
5.2 Adsorption kinetics 5.2.1 Modeling adsorption
The kinetics of adsorption may be controlled by several independent phenomena.
These can work in series or parallel and they often fall in one of the following general categories: bulk diffusion, external mass transfer (film diffusion), chemical reaction (chemisorption) and intraparticle diffusion (pore diffusion).
Several kinetic analyses are being applied to adsorption and not only they express the adsorption rates but also give indications of possible adsorption mechanisms.
[48]
5.2 Kinetics model used
Several simplified kinetics models are being used in researches. The most widely used are presented in the following chapters [46]. An example of a kinetic study is shown in Figure 11.
Figure 11. Results of adsorption studies of Pb(II), Cu(II) and Cd(II) on hydrogel [28].
5.2.1 Pseudo-first order kinetic model
The pseudo-first order kinetic model was presented by Lagergren [49]
[1 exp( )] (11)
where qt adsorption capacity at any timet
k1 pseudo-first order diffusion rate constant
t time.
5.2.2 Pseudo-second order kinetic model
The pseudo-second order kinetic model is described by the following equation [50]
= ) (12)
where k2 pseudo-second order rate constant.
Parameters for this equation can be derived by plotting t/qt against t. This model has been applied widely in the recent years to the adsorption of pollutants from wastewaters. The equation fitted to experimental batch operation data very well in large quantity of literature reported according to Ahmaruzzaman [5]. The rate expression is used to describe chemisorption. The main advantages of using pseudo-second order equation are that the initial rate of the adsorption and equilibrium concentration can be obtained from the model.
5.2.3 Intraparticle diffusion kinetic model
The intraparticle diffusion kinetic model was presented by Weber and Morris [51]
= , + (13)
where kid intra-particle diffusion rate constant Cid parameter.
Cid represents external convective mass transfer from the bulk liquid to the surface of the solid as it has same unit withqt, which gives an idea of the thickness of the boundary layer (the greater theCid the greater is the boundary layer effect).
These parameters are obtained by fitting qt against square root of time. If a good fit is obtained and if the plot passes through origin (Cid = 0), then according to Weber and Morris, the intra-particle diffusion is the rate limiting step. But if the plot yields multi-linear proportions, there are several rate limiting steps in the adsorption.
5.2.4 Elovich equation
The Elovich equation [52 ] is presented by equation (14)
= ln( ) + ln( )
(14)
where uE desorption constant m initial adsorption rate
qt amount of metal removed at timet
The Elovich equation parameters m and u can be obtained by plotting qt against ln(t). The equation is useful for determining the initial adsorption rate.
In general it should be noted that analysis of results from different kinetics models is somewhat neglected in many studies.
5.3 Breakthrough curve
Fixed-bed columns are used in the majority of large-scale applications of the adsorption processes. The behavior of fixed-bed column is often illustrated with breakthrough curves, like presented in the Figure 12. Adsorbent material is packed in a column and fluid flows continuously through the column where dynamic adsorption takes place. As the process continues, the amount adsorbed on top of the column becomes in equilibrium with the adsorbate influent concentration. This is called the saturation zone. Thereafter can be observed a region with increasing concentration of the adsorbate in which the mass transfer occurs, also called as the mass transfer zone (MTZ), or sometimes referred as the shock wave front. The depth of this zone is controlled by many variables such as characteristics of the adsorbate and the adsorbent, flow velocities and bed height.
This zone advances to the bottom of the column where the adsorbate concentration in the fluid starts to rise gradually. This breakthrough point eventually turns into exhaustion point. Normally the breakthrough curve takes an S-shape. Systems with high film transfer coefficients, high internal diffusivities or favorable isotherms result steeper slopes. [18]
Figure 12. Idealized breakthrough curve [39].
It should be noted that the effluent contains always some amounts of adsorbate and the theoretical equilibrium concentrations is rarely achieved in real situations.
Term minimal effluent concentration is defined as the average concentration of the metal ion in the effluent at the initial constant phase [20].
The mass transfer resistance and the axial mixing in real systems lead to deviations from the equilibrium theory. In systems with favorable isotherms the shock wave front is replaced by a term called constant pattern behavior. The concentration profile spreads in the initial region until stable situation is achieved.
At this point the mass transfer occurs at the same rate at every point along the wave front. This means that the shape of the mass transfer zone remains unaltered for majority of the bed. [8]
6 FACTORS AFFECTING ADSORBTION EQUILIBRIA
It is absolutely crucial to recognize that the adsorption equilibria is a very complicated phenomena. The adsorption capacities of the adsorbnets presented in this study are only strong indications of the uptakes and they can differ substantially in different conditions.
6.1 Effect of pH
According to Kocaobaet al. [53] it is generally accepted that adsorption of heavy metals increases by increasing the pH value. Most of the heavy metals form precipitates at pH higher than 6 and results of adsorption studies are no longer
reliable. Ahmaruzzaman [5] reported on industrial wastes as adsorbents that in certain pH range most metal adsorption increases with increasing pH up to a certain value. This can be explained with changes in the surface charge of the adsorbent and the metal species with changing pH values. When both of these surface charges become negative, the adsorption will decrease significantly. This is not the case for some heavy metals that exist as negative ions in solutions, such as chromium. Chromium may release hydroxide (OH-) instead of proton (H+) when adsorbed in certain materials.
It is known that cupper exists in various forms in an aqueous environment. Those forms are Cu2+, CuOH+, Cu(OH)20
, Cu(OH)3- and CU(OH)42-
as shown in the following equations
( ) ( ) + 2 (15)
+ (16)
+ ( ) ( ) (17)
( ) ( )+ ( ) (18)
( ) + ( ) (19)
Within pH 3 - 6 Cu2+ is the most dominant species in the solution while if the pH is above 6, the Cu(OH)2(s) starts to precipitate, depending on the concentration of solution (for example, 100 mg/L solution: the precipitation point is at pH 6.10).
Kumaret al. [12] reported that increasing pH resulted better adsorption capacities of Cu for aniline formaldehyde coated silica gel. At initial concentration of 100 mg/L, the capacities rise from 5.8 mg/g to 20.4 mg/g when pH increased from 5.4 to 6.0.
Krusic et al. [27] removed lead ions for water by poly(acrylamide-co-sodium methacrylate) (AAm/SMA ) hydrogels and investigated effect of pH in the range 2.0 – 6.0. At pH 5 the solubility of Pb(OH)2 is high and Pb2+ ions are the main species in the solution. The pH higher than 6 was not investigated to avoid precipitation of Pb. The adsorption capacity increased with increasing pH;
reaching the optimal value at pH 5.0, as indicated in the Figure 13.
Figure 13. The effect of pH on adsorption capacity of Pb2+ ions onto AAm/SMA hydrogels. [27]
Kurniawanet al. [33] noted that activated carbon performs efficiently at acidic pH range (2.5 to 7.0) and has the ability to treat wastewaters with metal concentration ranging from to 10 to 1000 mg/L.
Bhattacharyya and Gupta [35] reported that the number of available hydrogen ions is high at low pH. Cu2+ ions have to compete with them for the adsorption sites, which are weakly acidic in nature. Thus increasing pH, the active sites become gradually deprotonated and favor more and more Cu2+ uptake. According to Bhattacharya and Gupta [35], similar behavior has been reported by various other authors.
6.2 Effect of initial metal ion concentration
Generally the adsorption uptake rate is increased with increasing metal concentration of the heavy metals. Overcoming the mass transfer limitations is the primary reason for this behavior [5]. Erdem et al. [10] claimed that metal adsorption removal percentage decreases with increasing metal concentration by natural zeolite (the studied heavy metals were Cu, Co, Zn and Mn). This was an indication of that less energetically favorable sites take part in the adsorption mechanism. For example the adsorption percentage for copper ions decreased from over 65% to a slightly over 20% when the initial metal concentration was increased from 100 to 400 mg/L.
Dwivedi et al. [18] investigated the effect of initial lead ion concentration to breakthrough curve shapes in their column studies for Pb2+ removal. They found out that the larger the initial concentration, the steeper is the slope breakthrough curve and the time to reach breakthrough time is smaller. This is shown in the Figure 14. The diffusion process is concentration dependent and as the initial metal concentration increases, the metal loading rate increases. In the same time the driving force of the mass transfer increases, which results decrease in the adsorption zone length (steeper slope).
Figure 14. Breakthrough curve for different feed concentrations at constant hydraulic loading rate of 12 m3/(h m2) with granular activated carbon adsorbent. [18]
6.3 Effect of temperature
The majority of the conducted studies in the literature lack the temperature dependency studies. One probable reason for this is the fixed temperature of many applications (industrial effluents etc.). However, temperature dependency studies reveal a lot from the mechanism and the nature of the adsorption. Thermodynamic parameters like Gibbs free energy, entropy and enthalpy can be obtained from from isosteric experiments (qe is calculated from adsorption isotherms at different temperatures andqe is kept as constant) using equation (20). [54]
= + (20)
where Kd distribution coefficient of the adsorbate (qe/ce)
S change in entropy H change in enthalpy.
Thermodynamic parameters are calculated by plotting ln(Kd) versus 1/T. The values for Gibbs energy can be computed from the Gibbs relation (21):
= (21)
where G Gibbs free energy.
When deriving the values of thermodynamic properties, it is assumed that the enthalpy doesn’t change with temperature.
The dominant trend seems to be that the uptake of heavy metals from water rises with increasing temperature. Typical result for temperature dependency study is presented in the Figure 15.
Figure 15. Adsorption of copper ions to montmorillonite (clay 2 g/L; initial Cu(II) concentration 10, 20, 30, 40, 50 mg/L; pH 5.7; time 360 min) [35].
Bhattacharyya and Gupta [35] concluded that adsorption of Cu2+ on clay increases with increasing temperature, as shown in Figure 15. First possibility is that the copper ions overcome the activation energy of attaching to the surface more readily in higher temperatures. The second possibility arises from dissociation of the surface components of clay created by the additional adsorption sites.
Endothermic adsorption was suggested although thermodynamic data in other sources was rather scarce and didn’t fully match the case.
Krusic et al. [27] found that increase in temperature from 25 °C to 45 °C, adsorption capacity increased slightly for AAm/SMA hydrogel removal of lead ions. This was attributed to higher swelling (increase in porosity, total volume and active sites in the adsorbent) and decrease in the boundary layer thickness of the sorbent. Kocaoba [55] observed also only slight improvement in adsorption capacity (temperature range 20 – 60 °C) with Pb(II) and Cd(II) removal by dolomite. The adsorption was endothermic reaction and this was suggested to be the main reason for the behavior.
6.4 Mode of operation
Kurniawan et al. [33] reported some studies (Cu2+ removal with peanut hull for example), which showed significant improvements in adsorption capacities in column mode compared to batch studies results (65.6 mg/g and 10.2 mg/g, respectively). This behavior was explained by the different natures of column and batch studies. The concentration gradient decreases with time in batch experiments. In column operation, the adsorbent is continuously in contact with fresh feeding solution at the interface of the adsorption zone.
On the other hand, Dwivedi et al. [18], indicated that the adsorption capacity of GAC was far less in column mode than in batch mode. The maximum adsorption capacity achieved was in batch studies 26.5 mg/d and in column studies 2.0 mg/g (breakthrough capacity 50%). The explanation may lie with the potential irreversibility of the adsorption process. Another reason might be the different approaches to adsorption equilibrium in different systems. In bathc-mode the concentration in solution is continuously decreasing while in the column system the concentration is continuously increasing.
6.5 Effect of agitation speed and flow rate
In batch studies the greater the agitation speed the faster is the metal uptake rate.
This is related to mass transfer resistance. Reducing the film boundary layer surrounding particles, thus increasing the external film transfer coefficient and the rate of metal uptake [53]. In batch studies the time is rarely limited, but this is not the case with column studies. Dwivedi [18] concluded that increase in the flow rate in the column (also called as hydraulic loading rate) causes increase in the zone speed. As a result the time required to achieve breakthrough is decreased.
This causes variation in the slope of the breakthrough curve and adsorption uptake, as shown in Figure 16. Flow rates varied from 4 to 16 m3/(h m2), with the maximum adsorption uptake was at flow rate value of 12 m3/(h m2).
Figure 16. Breakthough curve for different hydraulic loading rates at constant feed concentration of 60 mg/L for Pb(II) removal with granular activated carbon [18].
6.6 Other factors affecting adsorption equilibria
Ahmaruzzaman [5] reported that decrease in particle size leads to increase in surface area and adsorption rate. Increase in surface area creates greater opportunities for binding heavy metals on the surface of the adsorbent. It also decreases intra-particle diffusional resistance, which is higher for larger particles.
Smaller particle size increases the adsorption capacity. This becomes with the price of difficult separation of adsorbent from solution or, in the case of columns, increase in pressure drop.
Ionic strength affects the affinity between the solute and the aqueous phase. It is one important factor influencing equilibrium. In general, increasing ionic strength decreases adsorption in aqueous solution. This is especially true if the adsorption is electrostatic attraction in nature. Some inorganic anions may form complexes with some metal ions affecting adsorption. [5]
Kurniawanet al. [33] reported that due their small ionic radius, the Cu ions had the highest uptakes among Cu, Ni, Mn and Co removal by kaolinite. The amount of Pb(II) adsorbed was more than Cu(II) or Cd(II) in the study of Wanget al. [28].
This was suggested to be related to the atomic radius, which is slighty smaller for lead than for copper or cadmium. The atomic radius affects diffusivity of the metal ions and availability of sites on the surface. In another study of kaolinite, Cr(II) ions were the most readily adsorbed among the selected heavy metals (Cd2+, Cr3+, Cu2+, Ni2+, Zn2+) due to its highest ionic charge compared to the others.
Erdem et al. [10] concluded from the adsorption capacities of several metal(II)ions onto zeolites, that the adsorption capacities obeyed the order of the diameter of the metal ions. The biggest diameter of the ions had the maximum adsorption capacity. An et al. [23] concluded this same result with crab shell adsorbent (order of adsorption was Pb>Cu>Cd) and it was stated that the heavy metal removal was correlated by electronegativity of the ions.
One feature affecting adsorption equilibria is surface charge of the adsorbent, which is affected strongly by pH. Kurniawan [33] reported several cases, where the modification of the adsorbent resulted higher adsorption capacities. It was suggested that the main factor for this behavior was the increased negative surface charge of the adsorbent.
It should strongly emphasized that the focus of this study was on single- component adsorption. The behavior of multicomponent (or real) adsorption is vital in design of adsorption processes, but was excluded nevertheless from this study.
7 SIMULATION OF AN ADSORPTION COLUMN 7.1 General procedure of design
According to Deliyanni et al. [48] the major aim in designing an adsorption column is to predict the service time until the column effluent exceeds the maximum allowed pollutant concentration. The maximum effluent concentration is in many cases defined by environmental regulations. The real problem with sizing the equipment accurately is that the progress of the mass transfer zone (MTZ) introduces time into the equations. To solve these kinds of problems, it is
needed to introduce set of partial differential equations that describe the heat and mass transfer phenomena. Several shortcut methods are available but the accuracy of those methods varies. The made simplifications and the uncertainties in them often relates to conservative sizing of equipment. Various methods have been suggested for designing fixed-bed adsorption systems. The length of unused bed (LUB) theory, empty bed residence time procedure (EBRT or EBCT) are some of the most common ones employed.
7.1.1 Length of Unused Bed
The constant pattern approximation provides a simple tool for the widely used LUB theory in design. The length of the capacity of the bed that is lost as a result of the spread in concentration profile is called the length of unused bedLUB. It can be calculated via the following two equations
= (1 ) (22)
= (1 ) (23)
where qb adsorption capacity in breakthrough point
L length of column
tb breakthrough time tst stoichiometric time.
The stoichiometric time describes the time needed for a stoichiometric front (the ideal case of no mass transfer resistance) to reach the end of the fixed bed. The breakthrough time and the stoichiometric breakthrough time can be calculated from overall mass balance
= 1 + = (24)
= 1 + = (25)
where u superficial flow velocity in the bed porosity of the bed.
The LUB is easily determined from an experimental breakthrough curve and the length of the column can be simply calculated from equilibrium considerations, if the constant pattern behaviour is assumed. [8]
7.1.2 Bed Depth Service Time Model
The Bed Depth Service Time (BDST) model relates the service time of the column to the quantity of the adsorbent in the bed, which is directly proportional to the bed height. The quantity is used instead of the bed volume, because the quantity of the bed is more accurate to measure [48]. The model is based on the study of Bohart and Adams [56]. The linear relationship between service time and bed height is
= 1 (26)
where KBA rate constant.
The service time can be obtained with laboratory column experiments over a range of flow velocities. Hutchins [57] simplified the equation by writing it in linear form
= + (27)
where
= (28)
= 1 (29)
The parameters in Equation (26) can now be obtained by conducting experiments in different bed depths and monitoring the operating time to reach certain removal percentage of heavy metals. This is called the BDST plot and the obtained lines are called isoremoval lines. An example of the plot is shown in Figure 17. The obtained parameters can be used to design an adsorption column with different flowrates and initial concentrations. [20]
Figure 17. Bohart-Adams modelling at mini-column studies. Isoremoval lines for 20, 30 and 60% breakthrough for different bed heights. Feed concentration 6 mg/L, hydraulic loading rate 7.5 m3/(h m2) [20].
Other models to predict the breakthrough curve according to Singhet al. [58] are the models of Thomas [59], Yoon and Nelson [60], Clark [61] and Wolbroska [62].
7.1.3 Empty Bed Residence Time model
The Empty Bed Residence Time (EBRT) is widely used design method for sizing fixed bed adsorbers. The minimum bed length is achieved by optimising the rate of the adsorbent spent (the exhaustion rate) and the EBRT operating line diagram.
The data for this optimization is obtained by the BDST or some other model used to predict the breakthrough curves (see previous chapter for details). The needed adsorbent quantity can be calculated with pre-selected breakthrough time from the selected model. In order to obtain full bed capacity, the value of 50%
breakthrough is often used. This is based on the assumption that the S-shaped breakthrough curve is symmetrical in that point, which is often not the case. [48]
7.2 Mass transfer modeling
7.2.1 Basic equations for adsorption column
The equations presented in this chapter are described in the same manner as in the work of Reunanenet al. [63].
The mass balance for fixed bed column may be written as
+ = ( ) (30)
where c concentration in fluid
t time
u superficial velocity z location in the column
void fraction
cs adsorbate concentration in solids, and the concentration in the adsorbent can be calculated from
= ( ) (31)
where mean value of the concentration in the particle
s density of the solid
If effective solid diffusivity is assumed, the mass transfer rate from the surface of the particles into the particles per unit volume is equal to
= | (32)
where mass transfer rate in the unit volume of bed a particle surface per unit volume of bed
b density of the bed r particle radius
where the solid concentration on the surface of the particle is determined by the adsorption equilibrium. In this case, the Freundlich adsorption equilibrium (Equation (5)) was used and where the liquid concentration on the surface is calculated from the bulk liquid concentrations as
= ( ) (33)
where kf mass transfer coefficient of the fluid ci interface concentration
If the linear driving force assumption is used to describe the mass flow rate into the particle, then Equation (32) may be expressed the following way
= ( ) (34)
where Ds diffusivity in the solid dp particle diameter
qi concentration in the solids at the interface
where the solid-side mass-transfer coefficient ks is described by the term 10Ds/ds. [63]
The mass transfer coefficient between the fluid and the particles in packed bed is obtained from empirical correlations found in the literature. Fujiki et al. [64]
mentioned some widely used correlations in their study. These included empirical correlations from Wilson-Geankoplis, Carberry, Syohdia-Ramswami-Hougen and Wakao-Funazkri. The Wakao and Funanzkri [65] experimental correlation was used in this study. It is expressed with dimensionless numbers as
= = 2 + 1.1 / , (35)
where Sh Sherwood number
Sc Schmidt number
Rep particle Reynolds number Dm diffusivity in the fluid The particle Reynolds number is defined
= ( ) (36)
where f density of the fluid
f viscosity of the fluid.
Diffusivity in fluid can be calculated with general correlations from the literature [66]. The value for effective diffusivity cannot be solved theoretically and it must be calculated from experimental data. Deff can be determined by carrying out adsorption experiments in stirred vessels (batch study). These studies are conducted in controlled conditions and the value of Deff is obtained from the kinetic data (usually a plot time versus concentration/reduced concentration). The external film mass transfer is often negligible (with high stirring speeds), which
